37 citations · 124 across the 18 of their papers we have counts for
18 papers
Lipschitz minimality of Hopf fibrations and Hopf vector fields
Dennis DeTurck, Herman Gluck, Peter A. Storm
Given a Hopf fibration of a round sphere by parallel great subspheres, we prove that the projection map to the base space is, up to isometries of domain and range, the unique Lipsc…
Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties
Richard D. Canary, Peter A. Storm
The space AH(M) of marked hyperbolic 3-manifold homotopy equivalent to a compact 3-manifold with boundary M sits inside the PSL_2(C)-character variety X(M) of π_1(M). We study the…
Local rigidity of hyperbolic manifolds with geodesic boundary
Steven P. Kerckhoff, Peter A. Storm
Let W be a compact hyperbolic n-manifold with totally geodesic boundary. We prove that if n>3 then the holonomy representation of pi_1 (W) into the isometry group of hyperbolic n-s…
The curious moduli spaces of unmarked Kleinian surface groups
Richard Canary, Peter Storm
Fixing a closed hyperbolic surface S, we define a moduli space AI(S) of unmarked hyperbolic 3-manifolds homotopy equivalent to S. This 3-dimensional analogue of the moduli space M(…
Infinitesimal rigidity of a compact hyperbolic 4-orbifold with totally geodesic boundary
Tarik Aougab, Peter A. Storm
Kerckhoff and Storm conjectured that compact hyperbolic n-orbifolds with totally geodesic boundary are infinitesimally rigid when n>3. This paper verifies this conjecture for a spe…
From the hyperbolic 24-cell to the cuboctahedron
Steven P. Kerckhoff, Peter A. Storm
We describe a family of 4-dimensional hyperbolic orbifolds, constructed by deforming an infinite volume orbifold obtained from the ideal, hyperbolic 24-cell by removing two walls.…